The Extended Path (EP) approach is known to provide a simple and fairly accurate solution to large scaled nonlinear models. The main drawback of the EP approach is that the Jensen inequality is neglected, because future shocks are (deterministically) set to their expected value of zero. Previous contributions shown that the cost of this approximation is small compared to the cost of neglecting the deterministic nonlinearities. But the accuracy errors are significantly increased in the presence of binding constraints (such as a Zero Lower Bound on nominal interest rates). In this paper we propose a simple extension to the EP approach by considering that the structural innovations in t+1 are non zero and keeping the innovations in t+s (s>1) equal to their expected value of zero. We use a quadrature approach to compute the expectations under this assumption. We evaluate the accuracy of the Stochastic Extended Path approach on a Real Business Cycle model. The computing time of this approach is polynomial in the number of endogenous variables but exponential with respect to the number of structural innovations.

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